In triangle abc, ab=cb, m∠abc=4x-3 and m∠cab=x-3. what is m∠abc
To find the measure of angle ABC (m∠ABC), we need to use the fact that the sum of angles in a triangle is 180 degrees.
Given that AB = CB, we can conclude that angles ABC and BCA are congruent. Let's represent their measure as y.
We are also given that m∠ABC = 4x - 3 and m∠CAB = x - 3.
Thus, we can write the equation: (4x - 3) + (y) + (y) = 180
Simplifying this equation, we have: 4x - 3 + 2y = 180
To solve for y, we need another equation. Since we know that AB = CB, we can conclude that angles BAC and BCA are congruent. Let's represent their measure as z.
Now we can write the equation for angle BAC: (x - 3) + (z) + (y) = 180
Simplifying this equation, we have: x - 3 + z + y = 180
We don't have enough information to determine the value of z, so we cannot solve for y at this time. Therefore, we cannot determine the exact measure of angle ABC (m∠ABC) with the given information.